Jerry,
Most barrels I have turned, I've screwed up. Sometimes I think this is because the barrel steel was stressed, and I should have annealed the metal before turning.
The first time I turned a barrel, I turned and turned until it looked pretty good. Polished it all up nice, etc. When I looked through the bore, the bore was curved so bad, I could not see through, only saw light.
Now I think I would make sure the bore was straight to begin with, then turn some locations 8 or ten inches apart for a steady rest to ride on. If I was to do a real thin wall barrel, I would turn a mandrel or fill the bore with Cerro, as you suggested.